Problem: Given $ m \angle AOB = 6x + 17$, and $ m \angle BOC = 8x - 75$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 17} + {8x - 75} = {180}$ Combine like terms: $ 14x - 58 = 180$ Add $58$ to both sides: $ 14x = 238$ Divide both sides by $14$ to find $x$ $ x = 17$ Substitute $17$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 8({17}) - 75$ Simplify: $ {m\angle BOC = 136 - 75}$ So ${m\angle BOC = 61}$.